Details

Time bar (total: 47.5s)

sample182.0ms

Algorithm
intervals
Results
39.0ms57×body640valid
37.0ms41×body1280valid
25.0ms131×body80valid
8.0ms17×body320valid
4.0ms10×body160valid

simplify5.5s

Counts
1 → 1
Iterations
IterNodes
done5074
72839
6707
5278
4167
3113
268
134
017

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos (/ K 2.0)) J)
0.2b
(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
6.9b
(* (* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) -2.0) (* (cos (/ K 2.0)) J))
9.6b
(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite660.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×pow1
18×add-cbrt-cube
13×add-sqr-sqrt
12×*-un-lft-identity prod-exp
10×add-cube-cbrt
9×pow-prod-down cbrt-unprod
7×unpow-prod-down
4×sqrt-div associate-*r* associate-*l* associate-*l/ pow-exp sqrt-prod add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ *-commutative flip-+
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 82
Calls
4 calls:
17.0ms
(* (cos (/ K 2.0)) J)
42.0ms
(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
407.0ms
(* (* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) -2.0) (* (cos (/ K 2.0)) J))
188.0ms
(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
93.0ms
(* (cos (/ K 2.0)) J)
302.0ms
(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
443.0ms
(* (* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) -2.0) (* (cos (/ K 2.0)) J))
276.0ms
(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify2.9s

Counts
94 → 94
Iterations
IterNodes
done5000
21546
1514
0203

prune996.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.8b

localize97.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
6.9b
(* (* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) -2.0) (* (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))) (* (cbrt (cos (/ K 2.0))) J)))
9.6b
(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite826.0ms

Algorithm
rewrite-expression-head
Rules
46×pow1
45×add-exp-log
33×add-cbrt-cube
31×pow-prod-down prod-exp cbrt-unprod
9×*-un-lft-identity
8×add-sqr-sqrt
7×add-cube-cbrt
6×cbrt-prod
4×sqrt-div associate-*l/ sqrt-prod add-log-exp
2×flip3-+ pow1/3 flip-+
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* associate-*l* *-commutative distribute-lft-out
Counts
4 → 80
Calls
4 calls:
2.0ms
(cbrt (cos (/ K 2.0)))
2.0ms
(cbrt (cos (/ K 2.0)))
610.0ms
(* (* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) -2.0) (* (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))) (* (cbrt (cos (/ K 2.0))) J)))
205.0ms
(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
273.0ms
(cbrt (cos (/ K 2.0)))
295.0ms
(cbrt (cos (/ K 2.0)))
516.0ms
(* (* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) -2.0) (* (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))) (* (cbrt (cos (/ K 2.0))) J)))
282.0ms
(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify4.3s

Counts
92 → 92
Iterations
IterNodes
done5001
21590
1398
0153

prune795.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.8b

localize202.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (* (cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))))
15.2b
(cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
15.2b
(cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
15.2b
(cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite454.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
13×*-un-lft-identity
12×pow1 cbrt-prod
9×sqrt-pow1 flip3-+ pow1/3 flip-+
8×sqrt-div
7×add-sqr-sqrt add-cube-cbrt
4×add-exp-log frac-times add-cbrt-cube add-log-exp
3×distribute-lft-out
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 69
Calls
4 calls:
197.0ms
(sqrt (* (cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))))
83.0ms
(cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
82.0ms
(cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
88.0ms
(cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series1.9s

Counts
4 → 12
Calls
4 calls:
463.0ms
(sqrt (* (cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))))
479.0ms
(cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
451.0ms
(cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
517.0ms
(cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify4.7s

Counts
81 → 81
Iterations
IterNodes
done5000
43517
31066
2414
1212
0116

prune1.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.8b

localize172.0ms

Local error

Found 4 expressions with local error:

5.4b
(sqrt (+ (pow (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 3) (pow 1.0 3)))
5.9b
(sqrt (+ (* (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)) (- (* 1.0 1.0) (* (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))))
13.8b
(+ (* (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)) (- (* 1.0 1.0) (* (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
21.5b
(/ (* (* (sqrt (+ (pow (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 3) (pow 1.0 3))) -2.0) (* (cos (/ K 2.0)) J)) (sqrt (+ (* (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)) (- (* 1.0 1.0) (* (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
22×add-exp-log add-cbrt-cube
20×*-un-lft-identity
18×sqrt-prod
12×add-sqr-sqrt
10×add-cube-cbrt
9×add-log-exp
8×sqrt-div prod-exp cbrt-unprod
6×pow1 times-frac associate-/r*
5×cbrt-undiv flip3-+ div-exp flip-+ distribute-lft-out
4×unpow-prod-down cube-prod associate-*l/
2×rem-sqrt-square associate-+r+ sqrt-pow1 pow1/2 sum-log associate-/r/ associate-/l/
1×+-commutative associate-+r- sub-neg frac-2neg diff-log clear-num sum-cubes div-inv associate-/l*
Counts
4 → 88
Calls
4 calls:
420.0ms
(sqrt (+ (pow (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 3) (pow 1.0 3)))
134.0ms
(sqrt (+ (* (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)) (- (* 1.0 1.0) (* (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))))
85.0ms
(+ (* (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)) (- (* 1.0 1.0) (* (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
1.1s
(/ (* (* (sqrt (+ (pow (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 3) (pow 1.0 3))) -2.0) (* (cos (/ K 2.0)) J)) (sqrt (+ (* (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)) (- (* 1.0 1.0) (* (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))))

series4.7s

Counts
4 → 12
Calls
4 calls:
239.0ms
(sqrt (+ (pow (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 3) (pow 1.0 3)))
1.1s
(sqrt (+ (* (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)) (- (* 1.0 1.0) (* (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))))
682.0ms
(+ (* (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)) (- (* 1.0 1.0) (* (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
2.7s
(/ (* (* (sqrt (+ (pow (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 3) (pow 1.0 3))) -2.0) (* (cos (/ K 2.0)) J)) (sqrt (+ (* (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)) (- (* 1.0 1.0) (* (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))))

simplify5.5s

Counts
100 → 100
Iterations
IterNodes
done5006
22093
1522
0190

prune1.1s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 7.8b

regimes1.1s

Accuracy

10.4% (8.0b remaining)

Error of 17.0b against oracle of 9.0b and baseline of 18.0b

bsearch340.0ms

Steps
ItersRangePoint
10
5.74712572203528e+173
4.4391554391661806e+188
8.829662133181109e+179
5
-2.174952851585701e+242
-9.725979020885111e+241
-1.695779976879256e+242

simplify14.0ms

Iterations
IterNodes
done36
136
026

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.7s1490×body1280valid
1.6s1267×body640valid
965.0ms4331×body80valid
364.0ms599×body320valid
156.0ms313×body160valid